They gave you the answer below - diffraction. But a high aperture is often unnecessary for distance landscapes. The focal point is so far away that even f/2 results in a large portion of the scene in focus. Many times they're taken around whatever aperture is sharpest on the lens (often f/8 ish).
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rfuscaFeb 21 '12 at 7:10

One thing that you should realize is that smaller sensors give larger depth of field, so when you hear general advice (targeted for slr users) that you should set the aperture to f/11 or f/16 to get a wide depth of field, you can easily use a much larger aperture to get the same depth of field on a compact.
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PeteFeb 21 '12 at 7:54

4 Answers
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Images with your camera will start showing signs of diffraction around f/4 to f/5.6 due to the size of the sensor. Shooting at a significantly smaller aperture (like f/11) will only increase the diffraction problems. You'll lose resolution.

I was going to mention diffraction too but thought it only became a factor at smaller apertures of f/16+, so f/11 wouldn't be a problem. Never thought about the sensor size being an issue for it there. Good point....
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MikeFeb 20 '12 at 14:57

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An additional, small factor might be that if this were a hand-held photo the smaller f-stop would bring a longer exposure and thus more shake from you holding the camera.
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Patrick HughesFeb 20 '12 at 18:46

I don't think that as such it is the sensor size that is the determining factor. But smaller sensors give smaller focal lengths. And smaller focal lengths give a physically smaller aperture, e.g. at 7mm focal length (which I think would be normal on a compact), at f/11, you would have an aperture with a diameter at around 0.64mm, and that is going to generate huge diffraction.
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PeteFeb 21 '12 at 7:50

@Pete: Pixel density also matters. Even with an equal physical aperture size, the diffracted photons end up being distributed over a larger number of photosites because in a smaller sensor there are typically more photosites per unit area.
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JohannesDDec 4 '13 at 9:51

Lens manufacturers design their lenses to provide the sharpest definition at one stop down from maximum aperture. Or at least, they used to. As mentioned above, diffraction effects are also a factor, and are proportional (roughly) to f stop.

So for normal use, use Aperture Priority setting, set to widest minus one stop, and let the shutter speed be the variable. The plus is less camera shake effects, the minus is reduced depth of field close up.

Another factor that can be common (especially for quite a bit of the subject matter in the pictures you posted) is that even a fairly light breeze can move the subjects (especially leaves) around during the exposure. This can result in (at least parts of) a picture looking unsharp, even when/if you do everything else right (e.g., using a tripod to prevent camera shake).

It is correct that a smaller aperture (higher f number) results in greater front-to-back focus, whilst larger apertures (smaller f numbers) result in more selective focus.

There is, however, a tradeoff. With the smaller apertures, less light is let into the camera body and in order to compensate for this, the camera must do one of two things. a) slow the shutter speed, in order to collect more light, or b) increase the ISO to make the sensor more sensitive to the light it does receive. Possibly, your camera will do both.

You do not say whether your sample images above were taken on a tripod, though since they are framed ever so slightly differently, I'm guessing not. The lack of sharpness in the second photograph may be caused by camera shake, where the shutter was open longer than for the photo with the larger aperture. The longer shutter time would also accentuate and capture movement in the water, as opposed to the first shot which, with a faster shutter speed, 'froze' the water.

With all things being equal however, the photos should result with the same 'brightness'. Your second photo is clearly slightly overexposed, compared to the first. So I am wondering if in the first photo, your camera metered off the water, and the second metered off the trees.

Unfortunately it's difficult to identify the exact issues based on the two photos provided. Can you perhaps supply not only the f stop used, but also the shutter speed and ISO values? (This will be stored as metadata (called EXIF) in the photo file. Windows or Mac should display this when the file is selected in Explorer/Finder).

+1 for the ISO. Although diffraction seems to be the most obvious answer, at least from a theoretical point of view, a closer examination of the magnified images reveals that the main flaw of the second one is high ISO. Or, more specifically, overly aggressive noise reduction.
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Edgar BonetFeb 21 '12 at 8:57

Yeah - I did think about that, but then thought it's only a problem (with DSLR's) at a small f/number around 16/18 and above. Therefore I didn't mention it as he said he shot at f/11 and I thought that would be no problem. It never occurred to me that the smaller coolpix camera would be affected at a much 'larger' value. So I have learned something too...!
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MikeFeb 21 '12 at 9:02